Question

A plano-convex lens has diameter $5cm$ and its thickness at the centre is $0.25cm$ . If the speed of light inside the lens is $2\times 10^{8}m{s}^{-1}$ , then if the focal length (in $cm$ ) of the lens is $\frac{2525}{x}$ then find $x$ .

Answer 1

Answer: 100

R. I. of lens,
$\mu =\frac{c}{v}=\frac{3\times 10^8}{2\times 10^8}=\frac{3}{2}$
From $△ACO$, radius of curvature of lens is,
$R^2=R_1^2+(R-0.25{)}^2$
$\therefore R^2=(2.5{)}^2+(R-0.25{)}^2$
$\therefore R^2=6.25+R^2+0.0625-0.5R$
$\therefore 0.5R=6.3125$
$\therefore R=12.625cm$
$F=\frac{R}{\mu -1}=\frac{12.625}{\frac{3}{2}-1}=25.25cm=\frac{2525}{100}cm$